Search results
Results From The WOW.Com Content Network
propositional logic, Boolean algebra, first-order logic ⊤ {\displaystyle \top } denotes a proposition that is always true. The proposition ⊤ ∨ P {\displaystyle \top \lor P} is always true since at least one of the two is unconditionally true.
As the name suggests propositional logic is a branch of mathematical logic which studies the logical relationships between propositions (or statements, sentences, assertions) taken as a whole, and connected via logical connectives.
The two main types of mathematical logic are propositional logic and predicate logic. In propositional logic, connective logic symbols are mainly used whereas in predicate logic quantifiers logic symbols are used along with the connectives.
Propositional logic is a fundamental branch of mathematical logic that deals with propositions (statements that are either true or false) and their relationships. It uses logical connectives such as AND (∧), OR (∨), NOT (¬), IMPLIES (→), and IF AND ONLY IF (↔) to form compound propositions.
The following is a comprehensive list of the most notable symbols in logic, featuring symbols from propositional logic, predicate logic, Boolean logic and modal logic. For readability purpose, these symbols are categorized by their function into tables.
Logical Equivalence. Because ¬(p ∧ q) and ¬p ∨ ¬q have the same truth tables, we say that they're equivalent to one another. We denote this by writing. ¬(p ∧ q) ≡ ¬p ∨ ¬q. The ≡ symbol is not a connective. The statement ¬(p ∧ q) ↔ (¬p ∨ ¬q) is a propositional formula.
In propositional logic we work with six logical connective: negation, conjunction, inclusive disjunction, exclusive disjunction, conditional and biconditional.